Subgroups — C₂×#19143498 #25960902

Order 11008.

2666 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063332	C₂	1	2	yes	maximal, complemented
2	#19143498	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583021	C₂	1	4	yes	maximal, complemented
4	C₂×#14583016	C₂	1	4	yes	maximal, complemented
5	C₂×#14582948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582916	C₂	1	2	yes	maximal, complemented
7	C₂×#14582857	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#575	C₂	1	1	yes	maximal, characteristic
9	C₂×#13063332	—	2	2	no	—
10	C₂×#13063332	—	2	2	no	—
11	C₂×#13063332	—	2	8	no	—
12	C₂×#13063332	C₂²	1	4	yes	complemented
13	C₂×#13063332	C₂²	1	4	yes	complemented
14	C₂×#13063332	C₂²	1	16	yes	complemented
15	C₂²×#10621877	—	2	2	no	—
16	C₂²×#10621877	C₂²	1	2	yes	—
17	C₂³×C₄₃⋊C₈	—	2	2	no	—
18	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×#13063284	C₂²	1	1	yes	characteristic
20	#14583021	C₂²	1	32	yes	complemented
21	#14583016	C₂²	1	32	yes	complemented
22	#14582948	C₂²	1	8	yes	complemented
23	C₂×#13063261	C₂²	1	4	yes	complemented
24	#14582916	C₂²	1	16	yes	complemented
25	C₂×#13063252	C₂²	1	8	yes	complemented
26	#14582857	C₂²	1	8	yes	complemented
27	C₂×#13063235	C₂²	1	2	yes	complemented
28	C₂×C₈×Dic₄₃	C₂²	1	2	yes	complemented
29	C₂²×#41×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#575	C₄	1	8	yes	complemented
31	C₄₃×#575	C₂²	1	8	yes	—
32	C₂×#137×C₄₃	C₄	1	4	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₄₃	C₄	1	4	yes	complemented
34	C₂×#135×C₄₃	C₂²	1	4	yes	—
35	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	#13063332	—	2	16	no	—
37	#13063332	—	2	16	no	—
38	#13063332	—	2	8	no	—
39	#13063332	—	2	8	no	—
40	#13063332	C₂³	1	16	yes	complemented
41	#13063332	C₂³	1	16	yes	complemented
42	C₂×#10621877	—	2	2	no	—
43	C₂×#10621877	—	2	4	no	—
44	C₂×#10621877	—	2	4	no	—
45	C₂×#10621877	—	2	4	no	—
46	C₂×#10621877	—	2	16	no	—
47	C₂×#10621877	C₂³	1	4	yes	—
48	C₂×#10621877	C₂³	1	8	yes	—
49	C₂²×C₄₃⋊C₈	—	2	2	no	—
50	C₂²×C₄₃⋊C₈	—	2	4	no	—
51	C₂²×C₄₃⋊C₈	—	2	4	no	—
52	C₂²×C₄₃⋊C₈	—	2	16	no	—
53	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
54	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
55	C₂²×C₄₃⋊C₈	D₄	1	4	yes	—
56	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
59	#13063284	—	2	2	no	—
60	#13063284	C₂³	1	4	yes	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
63	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
64	#13063261	C₂³	1	16	yes	complemented
65	#13063252	C₂³	1	32	yes	complemented
66	#13063235	C₂³	1	8	yes	complemented
67	C₈×Dic₄₃	C₂³	1	8	yes	complemented
68	C₂×#41×C₄₃	—	2	2	no	—
69	C₂×#41×C₄₃	—	2	4	no	—
70	C₂×#41×C₄₃	—	2	2	no	—
71	C₂×#41×C₄₃	—	2	4	no	—
72	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
73	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
74	C₂×#41×C₄₃	C₂³	1	4	yes	—
75	C₂×#41×C₄₃	C₂³	1	8	yes	—
76	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
77	C₂²×D₄×C₄₃	—	2	2	no	—
78	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
79	C₂³×C₄×C₄₃	—	2	2	no	—
80	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	#137×C₄₃	C₂×C₄	1	32	yes	complemented
82	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	32	yes	complemented
83	#135×C₄₃	C₂×C₄	1	16	yes	—
84	#135×C₄₃	C₂³	1	16	yes	—
85	C₂×Q₁₆×C₄₃	C₂×C₄	1	4	yes	—
86	C₂×SD₁₆×C₄₃	C₂×C₄	1	8	yes	—
87	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
88	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
89	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
90	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
91	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
92	C₂⁴×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	#41	1	1	yes	characteristic
94	#41×C₄₃	—	2	8	no	—
95	#41×C₄₃	—	2	8	no	—
96	#41×C₄₃	—	2	8	no	—
97	#41×C₄₃	—	2	8	no	—
98	#41×C₄₃	—	2	4	no	—
99	#41×C₄₃	—	2	4	no	—
100	#41×C₄₃	—	2	8	no	—
101	#41×C₄₃	C₂²×C₄	1	8	yes	—
102	#41×C₄₃	C₂²×C₄	1	16	yes	—
103	#41×C₄₃	C₂⁴	1	8	yes	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	4	no	—
106	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	2	8	no	—
112	C₂×D₄×C₄₃	—	2	4	no	—
113	C₂×D₄×C₄₃	—	2	8	no	—
114	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
115	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	2	8	no	—
118	C₂²×C₄×C₄₃	—	2	8	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	#41	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
129	C₂²×Dic₄₃	—	2	2	no	—
130	Q₁₆×C₄₃	C₂²×C₄	1	16	yes	—
131	SD₁₆×C₄₃	C₂²×C₄	1	32	yes	—
132	D₈×C₄₃	C₂²×C₄	1	16	yes	—
133	M₁₆×C₄₃	C₂²×C₄	1	16	yes	—
134	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
135	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
137	C₂²⋊Dic₄₃	—	2	4	no	—
138	C₄⋊Dic₄₃	—	2	4	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	C₂⁴	1	4	yes	—
141	#10621877	—	2	8	no	—
142	#10621877	—	2	4	no	—
143	#10621877	—	2	16	no	—
144	#10621877	—	2	16	no	—
145	#10621877	C₂⁴	1	8	yes	—
146	C₂×C₄₃⋊C₈	—	2	8	no	—
147	C₂×C₄₃⋊C₈	—	2	4	no	—
148	C₂×C₄₃⋊C₈	—	2	16	no	—
149	C₂×C₄₃⋊C₈	—	2	16	no	—
150	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
155	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
158	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
159	C₂³×C₄₃	—	2	8	no	—
160	C₂³×C₄₃	—	2	4	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	8	no	—
163	C₂³×C₄₃	C₄×D₄	1	2	yes	—
164	C₂³×C₄₃	C₄×D₄	1	2	yes	—
165	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂³×C₄₃	C₂×#41	1	2	yes	—
167	Q₈×C₄₃	—	2	8	no	—
168	Q₈×C₄₃	—	2	4	no	—
169	Q₈×C₄₃	C₂³×C₄	1	8	yes	—
170	D₄×C₄₃	—	2	16	no	—
171	D₄×C₄₃	—	2	8	no	—
172	D₄×C₄₃	—	2	8	no	—
173	D₄×C₄₃	—	2	8	no	—
174	D₄×C₄₃	—	2	4	no	—
175	D₄×C₄₃	C₂³×C₄	1	8	yes	—
176	C₂×C₄×C₄₃	—	2	8	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	8	no	—
179	C₂×C₄×C₄₃	—	2	16	no	—
180	C₂×C₄×C₄₃	—	2	8	no	—
181	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
183	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
184	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
194	C₂×Dic₄₃	—	2	4	no	—
195	C₂×Dic₄₃	—	4	4	no	—
196	C₈×C₄₃	C₂³×C₄	1	8	yes	—
197	C₄₃⋊C₈	—	2	8	no	—
198	C₄₃⋊C₈	C₂²×D₄	1	2	yes	—
199	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
200	C₄₃⋊C₈	C₂²×D₄	1	2	yes	—
201	C₂×#2955	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	4	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	8	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	16	no	—
208	C₂²×C₄₃	—	4	8	no	—
209	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
210	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
213	C₄×C₄₃	—	2	8	no	—
214	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
216	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
218	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
219	Dic₄₃	—	4	4	no	—
220	C₂×#575	D₄₃	1	1	yes	characteristic
221	C₂²×#131	—	43	2	no	—
222	#2955	—	43	16	no	—
223	C₂×#444	—	43	4	no	—
224	C₂×#443	—	43	4	no	—
225	C₂×#430	—	43	1	no	—
226	C₂×#421	—	43	2	no	—
227	C₂×#405	—	43	1	no	—
228	C₂×C₄₃	—	2	1	no	—
229	C₂×C₄₃	—	2	4	no	—
230	C₂×C₄₃	—	2	1	no	—
231	C₂×C₄₃	—	4	8	no	—
232	C₂×C₄₃	#2955	1	2	yes	complemented
233	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
234	C₂²×#41	C₂×D₄₃	1	2	yes	—
235	#575	Dic₄₃	1	8	yes	complemented
236	#575	C₂×D₄₃	1	8	yes	—
237	C₂×#137	Dic₄₃	1	4	yes	complemented
238	C₂×AGL(1,ℤ/8)	Dic₄₃	1	4	yes	complemented
239	C₂×#135	C₂×D₄₃	1	4	yes	—
240	C₂×#131	—	43	4	no	—
241	C₂×#131	—	43	4	no	—
242	C₂×#131	—	43	16	no	—
243	C₂×#131	—	86	2	no	—
244	C₂×#131	—	86	2	no	—
245	C₂×#131	—	86	8	no	—
246	C₂²×M₁₆	—	43	2	no	—
247	C₂²×M₁₆	—	86	2	no	—
248	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
249	C₂³×C₈	—	43	1	no	—
250	C₂³×C₈	—	86	2	no	—
251	C₂×#117	—	43	1	no	—
252	#444	—	43	32	no	—
253	#443	—	43	32	no	—
254	#430	—	43	8	no	—
255	C₂×#108	—	43	4	no	—
256	#421	—	43	16	no	—
257	C₂×#104	—	43	8	no	—
258	#405	—	43	8	no	—
259	C₂×#97	—	43	2	no	—
260	C₂×C₄×C₈	—	43	2	no	—
261	C₄₃	C₂×#2955	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	2	4	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	4	no	—
266	C₂×#41	C₂×Dic₄₃	1	4	yes	—
267	C₂×#41	C₂×Dic₄₃	1	8	yes	—
268	C₂×#41	C₂²×D₄₃	1	4	yes	—
269	C₂×#41	C₂²×D₄₃	1	8	yes	—
270	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
275	#137	C₂×Dic₄₃	1	32	yes	complemented
276	AGL(1,ℤ/8)	C₂×Dic₄₃	1	32	yes	complemented
277	#135	C₂×Dic₄₃	1	16	yes	—
278	#135	C₂²×D₄₃	1	16	yes	—
279	C₂×Q₁₆	C₂×Dic₄₃	1	4	yes	—
280	C₂×SD₁₆	C₂×Dic₄₃	1	8	yes	—
281	C₂×D₈	C₂×Dic₄₃	1	4	yes	—
282	#131	—	43	16	no	—
283	#131	—	43	16	no	—
284	#131	—	86	16	no	—
285	#131	—	86	16	no	—
286	#131	—	86	8	no	—
287	#131	—	86	8	no	—
288	C₂×M₁₆	—	43	4	no	—
289	C₂×M₁₆	—	43	8	no	—
290	C₂×M₁₆	—	86	16	no	—
291	C₂×M₁₆	—	86	4	no	—
292	C₂×M₁₆	—	86	4	no	—
293	C₂×M₁₆	—	86	4	no	—
294	C₂×M₁₆	—	86	2	no	—
295	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
296	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
297	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
298	C₂²×C₈	—	43	2	no	—
299	C₂²×C₈	—	43	2	no	—
300	C₂²×C₈	—	43	4	no	—
301	C₂²×C₈	—	43	1	no	—
302	C₂²×C₈	—	43	1	no	—
303	C₂²×C₈	—	43	4	no	—
304	C₂²×C₈	—	86	16	no	—
305	C₂²×C₈	—	86	4	no	—
306	C₂²×C₈	—	86	4	no	—
307	C₂²×C₈	—	86	2	no	—
308	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
309	#117	—	43	4	no	—
310	#117	—	86	2	no	—
311	C₂×C₄⋊C₄	—	86	1	no	—
312	C₂×C₂²⋊C₄	—	86	1	no	—
313	C₂×C₄²	—	43	2	no	—
314	#108	—	43	16	no	—
315	#104	—	43	32	no	—
316	#97	—	43	8	no	—
317	C₄×C₈	—	43	8	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	#10621900	1	1	yes	characteristic
320	#41	—	2	8	no	—
321	#41	—	2	8	no	—
322	#41	—	2	8	no	—
323	#41	—	2	8	no	—
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	8	no	—
327	#41	C₂²×Dic₄₃	1	8	yes	—
328	#41	C₂²×Dic₄₃	1	16	yes	—
329	#41	C₂³×D₄₃	1	8	yes	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
333	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
341	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	86	2	no	—
348	C₂²×C₄	D₄×D₄₃	1	2	yes	—
349	C₂²×C₄	D₄×D₄₃	1	2	yes	—
350	C₂²×C₄	#10621900	1	1	yes	characteristic
351	C₂²×C₄	#10621900	1	2	yes	—
352	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
353	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
354	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
355	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
356	Q₁₆	C₂²×Dic₄₃	1	16	yes	—
357	SD₁₆	C₂²×Dic₄₃	1	32	yes	—
358	D₈	C₂²×Dic₄₃	1	16	yes	—
359	M₁₆	—	43	8	no	—
360	M₁₆	—	86	16	no	—
361	M₁₆	—	86	16	no	—
362	M₁₆	—	86	8	no	—
363	M₁₆	—	86	4	no	—
364	M₁₆	C₂²×Dic₄₃	1	16	yes	—
365	C₂×C₈	—	43	8	no	—
366	C₂×C₈	—	43	8	no	—
367	C₂×C₈	—	43	2	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	43	1	no	—
370	C₂×C₈	—	43	2	no	—
371	C₂×C₈	—	43	1	no	—
372	C₂×C₈	—	43	2	no	—
373	C₂×C₈	—	43	2	no	—
374	C₂×C₈	—	86	16	no	—
375	C₂×C₈	—	86	16	no	—
376	C₂×C₈	—	86	8	no	—
377	C₂×C₈	—	86	4	no	—
378	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
379	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
380	C₂×C₈	C₂³×D₄₃	1	4	yes	—
381	C₄⋊C₄	—	86	4	no	—
382	C₂²⋊C₄	—	86	4	no	—
383	C₄²	—	43	4	no	—
384	C₄²	—	86	2	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	8	no	—
389	C₂³	D₄×Dic₄₃	1	2	yes	—
390	C₂³	D₄×Dic₄₃	1	2	yes	—
391	C₂³	C₂×#10621900	1	1	yes	characteristic
392	C₂³	C₂×#10621900	1	2	yes	—
393	Q₈	—	2	8	no	—
394	Q₈	—	2	4	no	—
395	Q₈	C₂³×Dic₄₃	1	8	yes	—
396	D₄	—	2	16	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	8	no	—
400	D₄	—	2	4	no	—
401	D₄	C₂³×Dic₄₃	1	8	yes	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	16	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	86	4	no	—
408	C₂×C₄	—	172	4	no	—
409	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
410	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
411	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
412	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
413	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
416	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
417	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
420	C₂×C₄	C₂×#10621900	1	2	yes	—
421	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
422	C₈	—	43	2	no	—
423	C₈	—	43	4	no	—
424	C₈	—	43	2	no	—
425	C₈	—	86	8	no	—
426	C₈	C₂³×Dic₄₃	1	8	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	16	no	—
433	C₂²	—	4	8	no	—
434	C₂²	C₂×D₄×Dic₄₃	1	4	yes	—
435	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
436	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
437	C₂²	C₂²×#10621900	1	1	yes	characteristic
438	C₄	—	2	8	no	—
439	C₄	—	172	4	no	—
440	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
441	C₄	C₂×D₄×Dic₄₃	1	4	yes	—
442	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
443	C₄	C₂⁴×Dic₄₃	1	1	yes	characteristic
444	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	4	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	8	no	—
449	C₂	#19143498	1	2	yes	direct product factor
450	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂×C₄₃×#575	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#575	D₄₃
hypocenter	C₄₃	C₂×#2955
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#575

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#13063332	C₂	semidirect
2. #19143498	C₂	direct (N × H)
3. C₂×#14583021	C₂	semidirect
4. C₂×#14583016	C₂	semidirect
5. C₂×#14582948	C₂	semidirect
6. C₂×#14582916	C₂	semidirect
7. C₂×#14582857	C₂	semidirect
12. C₂×#13063332	C₂²	semidirect
13. C₂×#13063332	C₂²	semidirect
14. C₂×#13063332	C₂²	semidirect
20. #14583021	C₂²	semidirect
21. #14583016	C₂²	semidirect
22. #14582948	C₂²	semidirect
23. C₂×#13063261	C₂²	semidirect
24. #14582916	C₂²	semidirect
25. C₂×#13063252	C₂²	semidirect
26. #14582857	C₂²	semidirect
27. C₂×#13063235	C₂²	semidirect
28. C₂×C₈×Dic₄₃	C₂²	semidirect
30. C₄₃×#575	C₄	semidirect
32. C₂×#137×C₄₃	C₄	semidirect
33. C₂×AGL(1,ℤ/8)×C₄₃	C₄	semidirect
40. #13063332	C₂³	semidirect
41. #13063332	C₂³	semidirect
64. #13063261	C₂³	semidirect
65. #13063252	C₂³	semidirect
66. #13063235	C₂³	semidirect
67. C₈×Dic₄₃	C₂³	semidirect
81. #137×C₄₃	C₂×C₄	semidirect
82. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
232. C₂×C₄₃	#2955	semidirect
235. #575	Dic₄₃	semidirect
237. C₂×#137	Dic₄₃	semidirect
238. C₂×AGL(1,ℤ/8)	Dic₄₃	semidirect
261. C₄₃	C₂×#2955	semidirect
275. #137	C₂×Dic₄₃	semidirect
276. AGL(1,ℤ/8)	C₂×Dic₄₃	semidirect
449. C₂	#19143498	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13063332	2
#19143498	2
C₂×#14583021	2
C₂×#14583016	2
C₂×#14582948	2
C₂×#14582916	2
C₂×#14582857	2
C₂×C₄₃×#575	2
C₂×#2955	43

Subgroups — C2×#19143498 #25960902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143498 #25960902